Applied Math PhD comprehensive exam | Sepideh Afshar, Lithium-Ion battery SOC estimation

Lithium-Ion battery SOC estimation

In recent years, electric and hybrid vehicles (EV/EHV) are becoming more attractive because of higher fuel efficiency and lower emissions. Batteries are the storage unit of electric vehicles and cells are their elementary units. Tracking the state-of-charge (SOC) of each cell in a battery pack is a key requirement for calculating the vehicle's range and driver's peace of mind. Although direct and precise measurement of SOC of a cell is not achievable by existing sensors, other quantities like battery terminal voltage and current can be easily measured. At every measurement step, the cells SOC is determined and updated via the available measurements.

The importance of accurate estimation of SOC is even more crucial in HEVs comparing to EVs since their environment characteristics are more demanding. Therefore, an appropriate method of more accurate estimation of SOC from available measurements are needed. In general, electrochemical model-based estimation methods provide higher accuracy; however, simplifying the governing equations is required to their complexity. So far, the simplified models in the literature lack the accuracy in estimatining SOC for chemical compositions like Lithium ion phosphate, LiFePO4, (LFP) at high current rates. The main weakness of these models is the poor approximation of cell's hysteretic behavior, a critical phenomenon in LFP cell's response.

As the first step of designing an observer, the electrochemical model must be studied for its important features including the nonlinearities, the properties of equilibrium points, and observability. The simplified model must preserve the affecting portion of the dynamics, the location and properties of the equilibrium points and the observability of the state vector. In this report,  the electrochemical governing equations are first simulated in COMSOL to investigate the existence of hysteresis in system response. After finding the equilibrium solutions of the system, a simplified model based on linearizing the system around some equilibrium points is developed. Next, sliding mode observer is introduced as a robust observer for SOC estimation.